Vectors
Core Idea
Vectors can be used to represent any set of objects that can be (a) added together, and, (b) multiplied by scalars to produce another object of the same type.
Intuitively, geometric vectors are familiar to us. They can be added to get another vector in the same space or can be scaled to get another vector in the same direction, scaled appropriately.
Similarly, it’s easy to see that polynomials can be qualified as vectors by this definition.
Elements in are tuples of size which could be added together (element-wise addition is familiar) and can be scaled linearly. Therefore they satisfy the requirements for a vector. Note that this addition to properly qualify the vector, we also need to formally define addition (reverse-one-and-add could also satisfy) as well as scalar multiplication to establish a vector.